Address:
Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
Faculty of Mathematics and Computer Sciences, Sabzevar Tarbiat Moallem University, Sabzevar, Iran
E-mail:
rsaadati@eml.cc
ghadir54@yahoo.com
Abstract: Let $X, Y$ be complex vector spaces. Recently, Park and Th.M. Rassias showed that if a mapping $f : X \rightarrow Y$ satisfies \begin{eqnarray} f(x+i y)+ f(x-iy) = 2 f(x) - 2f(y) \end{eqnarray} for all $x$, $y\in X$, then the mapping $f \colon X \rightarrow Y$ satisfies $f(x+y) + f(x-y) = 2 f(x) + 2 f(y)$ for all $x$, $y \in X$. Furthermore, they proved the generalized Hyers-Ulam stability of the functional equation () in complex Banach spaces. In this paper, we will adopt the idea of Park and Th. M. Rassias to prove the stability of a quadratic functional equation with complex involution via fixed point method.
AMSclassification: primary 39B72; secondary 47H10.
Keywords: quadratic mapping, fixed point, quadratic functional equation, generalized Hyers-Ulam stability.